r3

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course Mth 158

1/21 100 pm

If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution:

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

003. `* 3

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Question: * R.3.16 \ 12 (was R.3.6) What is the hypotenuse of a right triangle with legs 14 and 48 and how did you get your result?

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Your solution:

a^2 + b^2 = c^2

14^2 + 48^2 = c^2

196 + 2304 = 2500

Sqrt(2500) = c

c = 50

confidence rating #$&*: 3

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Given Solution:

* * ** The Pythagorean Theorem tells us that

c^2 = a^2 + b^2,

where a and b are the legs and c the hypotenuse.

Substituting 14 and 48 for a and b we get

c^2 = 14^2 + 48^2, so that

c^2 = 196 + 2304 or

c^2 = 2500.

This tells us that c = + sqrt(2500) or -sqrt(2500).

• Since the length of a side can't be negative we conclude that c = +sqrt(2500) = 50. **

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Question:

* R.3.22 \ 18 (was R.3.12). Is a triangle with legs of 10, 24 and 26 a right triangle, and how did you arrive at your answer?

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Your solution:

a^2 + b^2 = c^2

10^2 + 24^2 = 26^2

100 + 576 = 676

676 = 676

Yes the triangle is a right triangle I used the Pythagorean Theorem to solve this problem.

confidence rating #$&*:3

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Given Solution:

* * ** Using the Pythagorean Theorem we have

c^2 = a^2 + b^2, if and only if the triangle is a right triangle.

Substituting we get

26^2 = 10^2 + 24^2, or

676 = 100 + 576 so that

676 = 676

This confirms that the Pythagorean Theorem applies and we have a right triangle. **

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Self-critique (if necessary): ok

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Self-critique Rating:

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Question:

* R.3.34 \ 30 (was R.3.24). What are the volume and surface area of a sphere with radius 3 meters, and how did you obtain your result?

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Your solution:

Volume = 4/3 pi r^3

V = 4/3 pi (3 m)^3

V = 4/3 pi 27 m^3

V = 36 pi m^3

Surface Area = 4 * pi r^2

S = 4 * pi (3 m)^2

S = 4 * pi (9) m^2

S = 36 pi m^2

confidence rating #$&*: 3

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Given Solution:

* * ** To find the volume and surface are a sphere we use the given formulas:

Volume = 4/3 * pi * r^3

V = 4/3 * pi * (3 m)^3

V = 4/3 * pi * 27 m^3

V = 36pi m^3

Surface Area = 4 * pi * r^2

S = 4 * pi * (3 m)^2

S = 4 * pi * 9 m^2

S = 36pi m^2. **

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Self-critique (if necessary): ok

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Self-critique Rating:3

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Question:

* R.3.50 \ 42 (was R.3.36). A pool of diameter 20 ft is enclosed by a deck of width 3 feet. What is the area of the deck and how did you obtain this result?

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Your solution:

Area = pi r^2

Radius = diameter / 2 + the width of the deck

r = 10ft + 3ft = 13ft

a = pi (13 ft)^2

a = 169 pi ft^2

To find the area of the deck we just subtract the area of the pool from the center

169 pi ft^2 – 100 pi ft^2 = 69 pi ft^2

confidence rating #$&*:3

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Question:

* R.3.50 \ 42 (was R.3.36). A pool of diameter 20 ft is enclosed by a deck of width 3 feet. What is the area of the deck and how did you obtain this result?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Area = pi r^2

Radius = diameter / 2 + the width of the deck

r = 10ft + 3ft = 13ft

a = pi (13 ft)^2

a = 169 pi ft^2

To find the area of the deck we just subtract the area of the pool from the center

169 pi ft^2 – 100 pi ft^2 = 69 pi ft^2

confidence rating #$&*:3

#(*!

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Question:

* R.3.50 \ 42 (was R.3.36). A pool of diameter 20 ft is enclosed by a deck of width 3 feet. What is the area of the deck and how did you obtain this result?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Area = pi r^2

Radius = diameter / 2 + the width of the deck

r = 10ft + 3ft = 13ft

a = pi (13 ft)^2

a = 169 pi ft^2

To find the area of the deck we just subtract the area of the pool from the center

169 pi ft^2 – 100 pi ft^2 = 69 pi ft^2

confidence rating #$&*:3

#(*!#(*!

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